Approximately Optimal Subset Selection for Statistical Design and Modelling

TL;DR

This paper introduces an efficient polynomial-time algorithm based on Determinantal Point Processes for approximately solving the optimal subset selection problem, which maximizes the determinant of a positive definite matrix, with applications in various statistical domains.

Contribution

The paper develops a novel polynomial-time approximation algorithm for subset selection using DPPs, improving computational efficiency in statistical design and modeling.

Findings

Algorithm achieves near-optimal solutions efficiently

Demonstrated effectiveness on synthetic data

Validated on real-world datasets

Abstract

We study the problem of optimal subset selection from a set of correlated random variables. In particular, we consider the associated combinatorial optimization problem of maximizing the determinant of a symmetric positive definite matrix that characterizes the chosen subset. This problem arises in many domains, such as experimental designs, regression modeling, and environmental statistics. We establish an efficient polynomial-time algorithm using Determinantal Point Process for approximating the optimal solution to the problem. We demonstrate the advantages of our methods by presenting computational results for both synthetic and real data sets.